Grade Level: 9-12 Topic: Relationships Between Trigonometric Functions
Objectives:
Students will understand that Trigonometry is a branch of Mathematics that deals mainly with right triangles, and the relationships between their sides and angles.
Students will know important formulas: sin, cos, tan, cot, sec, csc.
Students will be able to show the relationships between the six trigonometric functions.
Maine Learning Results Alignment
Maine Learning Results: Mathematics- C. Geometry
Geometric Figures
Grades 9-Diploma
3. Students understand and use basic ideas of trigonometry.
b. Use trigonometry to solve for missing lengths in right triangles.
Rationale: Being able to identify the relationships between the six trigonometric functions provides far a firm base that is essential to the further study of trigonometry. It is from this base, that students will begin to use and understand the basic ideas of trigonometry.
Assessment
Formative (Assessment for Learning)
Students will be introduced to the idea of trigonometry, and all of its important formulas and the relationships between these formulas. In ordering to show their understanding, students must create a flow sheet by the end of class illustrating these topics. Students will first work with a partner in order to brainstorm ideas for their flowcharts. After brainstorming for a few minutes, student will begin to work on their charts. Once students have worked on their charts for about 20 minutes, they will switch partners and discuss their charts so far. They will give and receive peer feedback before finishing the work on their flow charts. Allowing students to brainstorm amongst their peers allows them to think aloud, as well as open their minds to ideas they may not have heard of or thought about previously. It gives them an opportunity to discuss the lesson and put a perspective on it, producing higher quality, well thought out work. Also, while they are working in partners, I will be going around the room to observe the students conversations, giving additional feedback when appropriate.
Summative (Assessment of Learning)
Student will create a final product using the software Inspiration by organizing the information in the way that best makes sense to them. As long as they understand the information accurately, their flow charts are fine. After receiving peer feedback, students will post a final copy to their class blog with an explanation of why they chose to organize the functions this way, as well as turn in a hard copy at the end of class. Their flow charts will show the relationships between all six trigonometric functions. In order for students to adequately complete this chart, they must know all the important formulas, as well as the relationships between them. This product helps introduce students to trigonometry, and begins to develop the strong base needed to continue study in this field.
Integration
English- Students partake in class discussions and give peer feedback on each other's work. They will then use this feedback to improve their flow charts.
Art- Student are given free range over the program Inspiration to create their chart with as much or as little 'flair' as they would like to use.
Technology- Students will use the flow chart software Inspiration to produce their final drafts.
Groupings
Students will first pick a partner of their choice to brainstorm ideas with. It will be open discussion as students begin to unfold the relationships between the six trigonometric functions. After brainstorming, they will begin work on their drafts. 20 minutes or so after working quietly, they will again choose a partner, someone they have not yet worked with this year. They will then takes turns presenting their chart to their partner and having give feedback on the chart in regardless to clarity and accuracy.
Differentiated Instruction
Strategies
Logical- Students are uncovering logical relationships between the six trigonometric functions. Verbal- Students are brainstorming ideas with a partner, and giving peer feedback to their partner(s). Interpersonal- Students will be working with partners to brainstorm ideas, then collaborate with other partners in order to recieve feedback on their charts. Spatial- Students will be using Inspiration to visualize the relationships between the functions in such a way that they can easily understand. Intrapersonal- Students will be using Inspiration independently in order to create the final draft of their flow chart. Bodily-Kinesthetic- Students will be up and moving around during the Rethink and Revise stages as they switch partners and get materials to help them think.
Modifications/Accommodations
I will review student's IEP, 504, or ELLIDEP and make appropriate modifications and accommodations. Absent students are responsible for coming to see me during the next day that they are in class in order to recieve any make-up work. Upon meeting with me, I will decide, based upon any activities they missed, whether or not they must stay and make up time after school, or if an alternate assignment would be just as sufficient. Absent students have 3 days upon returning to school in order to make up missed work, or, under extenuating circumstances, to make arrangements with me as to when this work will be due. Absent students will lose points for classroom participation, but will be given the option of doing an alternate assignment of my choice in order to make up the lost points.
Extensions
Students will begin the lesson by comparing their similarities in order to fill in the flow chart at the front of the room. After students have fully grasped the idea of flow charts, they will use Inspiration to create a flow chart of the six trigonometric functions. They will pair up in order to provide/receive peer feedback. After creating their final draft, they will post the graphic to the class blog, along with a description of why they chose to organize the chart the way they did. By posting to the class blog, I am able to give them feedback that they can check anytime, as well as give and receive feedback with their peers. In this way, they have many opportunities for improvement.
Materials, Resources and Technology
Laptops with the program Inspiration fully installed
Scratch paper/flow charts for brainstorming
Internet access for posting work
Source for Lesson Plan and Research
Student will create a blogger account if they do not already have one and create a blog devoted to the class, where they will be required to post most assignments. www.blogger.com
Maine Standards for Initial Teacher Certification and Rationale
Standard 3 - Demonstrates a knowledge of the diverse ways in which students learn and develop by providing learning opportunities that support their intellectual, physical, emotional, social, and cultural development. Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by providing a flexibility for various learner opportunities. All students learn in a variety of ways, and by allowing peer feedback, as well as floating around the room to observe student interactions, the allows for a greater learning opportunities. Students will be given a list of the class's agenda [written on the board], the opportunity to go straight to experimenting with different flow chart techniques on their own, the chance for peer feedback from more than one student, and time to brainstorm ideas before diving in. These methods reflect all four learning styles, so students will strengths in any one or two areas will benefit from instruction.
Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory. Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by creating an atmosphere where students develop their higher level thinking. Students will be asked to create a flow chart linking together the 6 trigonometric functions in any way that is correct and makes logical sense to the student. To do so, they will need to be able to cover several steps. First, students will explain the six trigonometric functions. Next they will need to able to put this information into a flow chart by applying their knowledge of relationships to make connections between the functions. They will also create a statement describing how the chart is to interpreted based in the connections made to ensure student understanding. By allowing students to give feedback to one another, students will be able to see the functions from more than one point of view, which will help open them up while creating their one charts. In order for a student to understand the work of another student, they must develop empathy. And finally, this activity provides a variety of learning styles that will help students obtain a self-knowledge of how they work best.
Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs. Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by incorporating a variety of methods designed to speak to multiple intelligences in the classroom. Providing an opportunity for several intelligences in a classroom environment ensures that more students will be given a chance to show their strength and provide a better learning environment overall.
Logical- Students are uncovering logical relationships between the six trigonometric functions. Verbal- Students are brainstorming ideas with a partner, and giving peer feedback to their partner(s). Interpersonal- Students will be working with partners to brainstorm ideas, then collaborate with other partners in order to receive feedback on their charts. Spatial- Students will be using Inspiration to visualize the relationships between the functions in such a way that they can easily understand. Intrapersonal- Students will be using Inspiration independently in order to create the final draft of their flow chart. Bodily-Kinesthetic- Students will be up and moving around during the Rethink and Revise stages as they switch partners and get materials to help them think.
For each class period, students will post blog entry reflecting that days assignment. Peers will then be able to go onto the class blog to provide peer feedback to the student. If the student so chooses, they will be able to update the assignment before the next class period based in the peer feedback they received. The blog will include a post for each lesson, as well as their final assessment. Additional blogs maybe assigned at my discretion.
Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner. Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by providing students with several opportunities for feedback before the final product is submitted. Students will begin the activity by brainstorming ideas, then comparing brainstorming ideas with a partner of their choice. During both sessions I will be floating around the classroom to ensure that students grasp the concept between the six trigonometric functions, and are able to link them together in logical ways. As I float around, I will give feedback to the students when appropriate to keep them on the right track. After their flow chart is completed [if it is not done in class, it is assigned for homework], they will need to post it too the class week, where I will then grade the assignment. Student will them be given one final opportunity to gain additional points by updating the assignment based on peer feedback on their blog entries. They have until the next class period to do so. If they choose not to make any chance, then the final grade stays the same.
Teaching and Learning Sequence:
The classroom is set up in a horseshoe design, to focus student learning to the center of the room. Students will begin the day by doing a group activity, where they take turns writing on the board. The horseshoe set-up allows students the room needed for them to all be in front of the board and participate during the activity. A laptop cart will be brought into the room to allow students to use the software Inspiration. They will use laptops at their seats. Students will receive a warning before the end of the class period, so they can put laptops away correctly.
Agenda:
Hook students with flow chart activity (10 minutes)
Make sure all students have Blogger accounts (10 minutes)
Review trigonometric functions (8 minutes)
Pass out graphic organizers (2 minutes)
Allow students to brainstorm independently (10 minutes)
Students share ideas with a partner of their choice (5 minutes)
Students begin working with Inspiration (15 minutes)
Students explain flow chart to a different partner of their choice (10 minutes)
Flow chart not finished in class will be assigned for homework
Students given 10 minute warning before end of class to put laptops away and reminded to post flow chart to class blog by next class
Students will begin studying trigonometry which deals with relationships between the sides and angles of a right triangle. Students' understanding of this concept will be shown in their ability to create a flow chart connecting the six functions together. This lesson is essential to gain any further understanding of trigonometry a the year progresses. All lesson build upon each other and the idea that trigonometry is essential for many occupations to exist effectively. At the end of the unit students will be required to do a project on an occupation if their choice, and it integrates trigonometry into day to day work. As a hook, students will fill out a graphic organizer on the board that connects all of them into a flow chart. All connections must be kept positive and can be as creative as the students make it. This will give students an opportunity to play with the idea of a flow chart before they complete the class activity as well as open them up to several ways in which connections can be made. This lesson also speaks to a variety of student intelligences as I have mentioned earlier in the lesson plan [See rationale statement for standard 5]. Providing an opportunity for students to express their strengths throughout the their multiple intelligences allows a greater learning experiences for all students.
Students will know important formulas: sin, cos, tan, cot, sec, csc. These are the six trigonometric functions and, as implied, are the building blocks to understanding trigonometry as a whole. I will begin the lesson with a group activity so that all students understand what a flow chart is. After I have reviewed the six trigonometric functions and their characteristics, students will create a flow chart using Inspiration to help them apply their knowledge of the functions, as well as to create a system that is easy for them to remember the six trigonometric functions and how they are related, as that is a big part of trigonometry. To check for understanding, I will float around the room to observe student work and to ask them about their flow charts to make sure they are on the right track. I will give feedback when appropriate. For a detailed description of the content, see teacher notes.
Students will be able to show the relationships between the six trigonometric functions. As described earlier in the lesson, throughout the class period, students will progress though all stages of higher-level thinking. First, students will explain the six trigonometric functions. Next they will need to able to put this information into a flow chart by applying their knowledge of relationships to make connections between the functions. They will also create a statement describing how the chart is to interpreted based in the connections made to ensure student understanding. By allowing students to give feedback to one another, students will be able to see the functions from more than one point of view, which will help open them up while creating their one charts. In order for a student to understand the work of another student, they must develop empathy. And finally, this activity provides a variety of learning styles that will help students obtain a self-knowledge of how they work best. By using a series of flow charts students can begin to see the connections made between the different functions, and manipulate their relationships to create a system that is logical to them. Students will also work in pairs during part of the brainstorm activities in order to help develop their ideas by having to explain to another individual. Students will choose a partner of their choice to work with. Once in partners, students will take turns explaining the way they see the six functions being connected. During the first pairing, students will simply bounce ideas off of one-another for constructive feedback. During the second pairing, students will need explain the way in which they plan to finish their charts to explain the relationships between all the functions. Using the feedback from their peers, students are able to rethink their original flow chart ideas and revise their original charts before the final project is due. By having students explain their charts to a partner of their choice, they are able to rehearse the statement they are going to attach to the chart that explains how they put the chart together, and how the functions are related. Students are able to take the charts home to do for next class in order to refine them based on all of the feedback and support they received throughout the class period. They are then required to post the chart to class Blog for final grade. Based on peer feedback to the blog students will be given one final opportunity to refine their work for additional points. They do not have to work on the activity again after it has been posted to the Blog. If they choose not to turn in any additional work by next, then the original grade given stays. The final flow chart will be the students' evidence of learning for this activity. By creating an accurate flow chart, it shows that the students understand the relationships between the functions, and are able to apply this knowledge in creative ways.
Students will be able to take any feedback given to them by me or their peers and assess their flow chart in terms of accuracy and clarity. Students will be given several opportunities for feedback during class by their peers, as well as after class when students are required to post comments on the class blog as part of their homework assignment. Students will be able to use all of this feedback before a final grade is assigned to them for this activity. After posted to the class blog, I will also provide feedback to the student with the opportunity to refine the assignment for additional points. I will give feedback to the student by the next class day, and the revision made to the activity will be due the next class period after feedback on the blog is received. Learning the relationships between the six trigonometric functions will give the students a strong foundation for the next class period. During the next lesson students will need to derive all six functions from unit circle, which is impossible to do with first knowing each trigonometric function and it's properties. However, by giving students a strong knowledge of the characteristics of the six trigonometric functions allows them to better see how they are each derived from the unit circle. For a detailed explanation see the next lesson and it's teacher notes.
Evaluate, Refine, Tailor:Logical, Verbal, Interpersonal, Intrapersonal, Bodily-kinesthetic, and Spatial
UMF LESSON PLAN FORMAT
Teacher’s Name: Ms. Jess L Mitchell Lesson # : 1
Grade Level: 9-12 Topic: Relationships Between Trigonometric Functions
Objectives:
Maine Learning Results Alignment
Geometric Figures
Grades 9-Diploma
3. Students understand and use basic ideas of trigonometry.
b. Use trigonometry to solve for missing lengths in right triangles.
Rationale: Being able to identify the relationships between the six trigonometric functions provides far a firm base that is essential to the further study of trigonometry. It is from this base, that students will begin to use and understand the basic ideas of trigonometry.
Assessment
Students will be introduced to the idea of trigonometry, and all of its important formulas and the relationships between these formulas. In ordering to show their understanding, students must create a flow sheet by the end of class illustrating these topics. Students will first work with a partner in order to brainstorm ideas for their flowcharts. After brainstorming for a few minutes, student will begin to work on their charts. Once students have worked on their charts for about 20 minutes, they will switch partners and discuss their charts so far. They will give and receive peer feedback before finishing the work on their flow charts. Allowing students to brainstorm amongst their peers allows them to think aloud, as well as open their minds to ideas they may not have heard of or thought about previously. It gives them an opportunity to discuss the lesson and put a perspective on it, producing higher quality, well thought out work. Also, while they are working in partners, I will be going around the room to observe the students conversations, giving additional feedback when appropriate.
Student will create a final product using the software Inspiration by organizing the information in the way that best makes sense to them. As long as they understand the information accurately, their flow charts are fine. After receiving peer feedback, students will post a final copy to their class blog with an explanation of why they chose to organize the functions this way, as well as turn in a hard copy at the end of class. Their flow charts will show the relationships between all six trigonometric functions. In order for students to adequately complete this chart, they must know all the important formulas, as well as the relationships between them. This product helps introduce students to trigonometry, and begins to develop the strong base needed to continue study in this field.
Integration
Art- Student are given free range over the program Inspiration to create their chart with as much or as little 'flair' as they would like to use.
Technology- Students will use the flow chart software Inspiration to produce their final drafts.
Groupings
Differentiated Instruction
Logical- Students are uncovering logical relationships between the six trigonometric functions.
Verbal- Students are brainstorming ideas with a partner, and giving peer feedback to their partner(s).
Interpersonal- Students will be working with partners to brainstorm ideas, then collaborate with other partners in order to recieve feedback on their charts.
Spatial- Students will be using Inspiration to visualize the relationships between the functions in such a way that they can easily understand.
Intrapersonal- Students will be using Inspiration independently in order to create the final draft of their flow chart.
Bodily-Kinesthetic- Students will be up and moving around during the Rethink and Revise stages as they switch partners and get materials to help them think.
I will review student's IEP, 504, or ELLIDEP and make appropriate modifications and accommodations. Absent students are responsible for coming to see me during the next day that they are in class in order to recieve any make-up work. Upon meeting with me, I will decide, based upon any activities they missed, whether or not they must stay and make up time after school, or if an alternate assignment would be just as sufficient. Absent students have 3 days upon returning to school in order to make up missed work, or, under extenuating circumstances, to make arrangements with me as to when this work will be due. Absent students will lose points for classroom participation, but will be given the option of doing an alternate assignment of my choice in order to make up the lost points.
Students will begin the lesson by comparing their similarities in order to fill in the flow chart at the front of the room. After students have fully grasped the idea of flow charts, they will use Inspiration to create a flow chart of the six trigonometric functions. They will pair up in order to provide/receive peer feedback. After creating their final draft, they will post the graphic to the class blog, along with a description of why they chose to organize the chart the way they did. By posting to the class blog, I am able to give them feedback that they can check anytime, as well as give and receive feedback with their peers. In this way, they have many opportunities for improvement.
Materials, Resources and Technology
Scratch paper/flow charts for brainstorming
Internet access for posting work
Source for Lesson Plan and Research
www.blogger.com
Maine Standards for Initial Teacher Certification and Rationale
Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by providing a flexibility for various learner opportunities. All students learn in a variety of ways, and by allowing peer feedback, as well as floating around the room to observe student interactions, the allows for a greater learning opportunities. Students will be given a list of the class's agenda [written on the board], the opportunity to go straight to experimenting with different flow chart techniques on their own, the chance for peer feedback from more than one student, and time to brainstorm ideas before diving in. These methods reflect all four learning styles, so students will strengths in any one or two areas will benefit from instruction.
Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by creating an atmosphere where students develop their higher level thinking. Students will be asked to create a flow chart linking together the 6 trigonometric functions in any way that is correct and makes logical sense to the student. To do so, they will need to be able to cover several steps. First, students will explain the six trigonometric functions. Next they will need to able to put this information into a flow chart by applying their knowledge of relationships to make connections between the functions. They will also create a statement describing how the chart is to interpreted based in the connections made to ensure student understanding. By allowing students to give feedback to one another, students will be able to see the functions from more than one point of view, which will help open them up while creating their one charts. In order for a student to understand the work of another student, they must develop empathy. And finally, this activity provides a variety of learning styles that will help students obtain a self-knowledge of how they work best.
Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by incorporating a variety of methods designed to speak to multiple intelligences in the classroom. Providing an opportunity for several intelligences in a classroom environment ensures that more students will be given a chance to show their strength and provide a better learning environment overall.
Logical- Students are uncovering logical relationships between the six trigonometric functions.
Verbal- Students are brainstorming ideas with a partner, and giving peer feedback to their partner(s).
Interpersonal- Students will be working with partners to brainstorm ideas, then collaborate with other partners in order to receive feedback on their charts.
Spatial- Students will be using Inspiration to visualize the relationships between the functions in such a way that they can easily understand.
Intrapersonal- Students will be using Inspiration independently in order to create the final draft of their flow chart.
Bodily-Kinesthetic- Students will be up and moving around during the Rethink and Revise stages as they switch partners and get materials to help them think.
For each class period, students will post blog entry reflecting that days assignment. Peers will then be able to go onto the class blog to provide peer feedback to the student. If the student so chooses, they will be able to update the assignment before the next class period based in the peer feedback they received. The blog will include a post for each lesson, as well as their final assessment. Additional blogs maybe assigned at my discretion.
Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by providing students with several opportunities for feedback before the final product is submitted. Students will begin the activity by brainstorming ideas, then comparing brainstorming ideas with a partner of their choice. During both sessions I will be floating around the classroom to ensure that students grasp the concept between the six trigonometric functions, and are able to link them together in logical ways. As I float around, I will give feedback to the students when appropriate to keep them on the right track. After their flow chart is completed [if it is not done in class, it is assigned for homework], they will need to post it too the class week, where I will then grade the assignment. Student will them be given one final opportunity to gain additional points by updating the assignment based on peer feedback on their blog entries. They have until the next class period to do so. If they choose not to make any chance, then the final grade stays the same.
Teaching and Learning Sequence:
Agenda:
Students will begin studying trigonometry which deals with relationships between the sides and angles of a right triangle. Students' understanding of this concept will be shown in their ability to create a flow chart connecting the six functions together. This lesson is essential to gain any further understanding of trigonometry a the year progresses. All lesson build upon each other and the idea that trigonometry is essential for many occupations to exist effectively. At the end of the unit students will be required to do a project on an occupation if their choice, and it integrates trigonometry into day to day work. As a hook, students will fill out a graphic organizer on the board that connects all of them into a flow chart. All connections must be kept positive and can be as creative as the students make it. This will give students an opportunity to play with the idea of a flow chart before they complete the class activity as well as open them up to several ways in which connections can be made. This lesson also speaks to a variety of student intelligences as I have mentioned earlier in the lesson plan [See rationale statement for standard 5]. Providing an opportunity for students to express their strengths throughout the their multiple intelligences allows a greater learning experiences for all students.
What, Where, Why, Hook, Tailor: Logical, Verbal, Interpersonal, Intrapersonal, Bodily-kinesthetic, and Spatial
Equip, Tailor: Logical, Verbal, Interpersonal, Intrapersonal, Bodily-kinesthetic, and Spatial [See teacher Notes]
Explore, Experience, Rethink, Revise, Rehearse, Refine, Tailor: Logical, Verbal, Interpersonal, Intrapersonal, Bodily-kinesthetic, and Spatial
Evaluate, Refine, Tailor: Logical, Verbal, Interpersonal, Intrapersonal, Bodily-kinesthetic, and Spatial